Least Squares Orthogonal Distance Fitting of Curves and by Sung Joon Ahn

By Sung Joon Ahn

Due to the continued growth of sensor expertise, the provision of three-D c- eras is already foreseeable. those cameras are able to producing a wide set of size issues inside of a really short while. there's a number of 3-D digital camera - plications within the ?elds of robotics, quick product improvement and electronic factories. to be able to not just visualize the purpose cloud but additionally to acknowledge three-D item m- els from the purpose cloud after which extra strategy them in CAD structures, ef?cient and strong algorithms for 3-D info processing are required. For the au- matic segmentation and popularity of such geometric primitives as airplane, sphere, cylinder, cone and torus in a 3-D element cloud, ef?cient software program has lately been built on the Fraunhofer IPA by means of Sung Joon Ahn. This booklet describes intimately the full set of ‘best-?t’ algorithms for common curves and surfaces in house that are hired within the Fraunhofer software.

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Consequently, a series of international research projects was launched in order to establish an objective method for testing CMM software tools without requiring CMM manufacturers to disclose their software techniques (black-box approach). 1) Parameter estimation criterion: minimization of the square sum of predefined error measures (least-squares method [36]) Error measure definition: geometric distance between the test model feature and the given point [29], [58] Set of data points: rectangular coordinate values of a 2-D/3-D set of points emulating the real measurement points of the test model feature arbitrarily located and oriented in the predefined measurement volume [42], [81].

Sourlier [74] developed a new general ODF algorithm for parametric features X(a, u) with the grouping of the parameters of form, position, and rotation. A further advantage of this algorithm is the low implementation cost for a new model feature, because only the first derivatives of X(a, u) are required. The algorithm simultaneously determines the model parameters and the shortest distance points thus requiring considerable memory space and high computing cost if a sparse matrix algorithm is not used additionally.

The point measurement accuracy of the high-end products on the current CMM market is at the level of for a measurement volume of To retain the overall accuracy of CMM’s at a high level, the CMM software tool used for processing the measurement data must be at least 5–10 times more accurate than the point measurement accuracy of the host CMM. ISO 10360-6 gives full details of the accuracy evaluation and testing method for CMM software tools, without giving any indication of how to realize a highly-accurate CMM software tool.

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